An angle shows (2x + 3) and (x - 6). First, write an equation for these two supplementary angles. Then, explain how to solve for the value of x. Lastly, find the measurements of each angle. Make sure to list them both.
To write an equation for the two supplementary angles, we know that supplementary angles add up to 180 degrees. So, we can write the equation as:
(2x + 3) + (x - 6) = 180
To solve for the value of x, we need to simplify and solve the equation. First, let's combine the like terms on the left side:
3x - 3 = 180
Next, we can isolate the term with x on one side by adding 3 to both sides:
3x - 3 + 3 = 180 + 3
3x = 183
Finally, we can solve for x by dividing both sides by 3:
x = 61
Now that we have the value of x, we can find the measurements of each angle by substituting x = 61 into the angle expressions.
For the first angle:
2x + 3 = 2(61) + 3 = 122 + 3 = 125 degrees
For the second angle:
x - 6 = 61 - 6 = 55 degrees
So, the measurements of the two angles are 125 degrees and 55 degrees, respectively.